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A254333 Squares (A000290) which are also centered pentagonal numbers (A005891). 4
1, 16, 1156, 22801, 1666681, 32878756, 2403352576, 47411143081, 3465632747641, 68366835443776, 4997440018745476, 98584929298781641, 7206305041398228481, 142159399682007682276, 10391486872256226723856, 204993755756525779060081, 14984516863488437537571601 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Colin Barker, Table of n, a(n) for n = 1..634

Index entries for linear recurrences with constant coefficients, signature (1,1442,-1442,-1,1).

FORMULA

a(n) = a(n-1)+1442*a(n-2)-1442*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+15*x^3-302*x^2+15*x+1) / ((x-1)*(x^2-38*x+1)*(x^2+38*x+1)).

EXAMPLE

16 is in the sequence because it is the 4th square number and the 3rd centered pentagonal number.

MATHEMATICA

LinearRecurrence[{1, 1442, -1442, -1, 1}, {1, 16, 1156, 22801, 1666681}, 20] (* Harvey P. Dale, Jul 26 2015 *)

PROG

(PARI) Vec(-x*(x^4+15*x^3-302*x^2+15*x+1) / ((x-1)*(x^2-38*x+1)*(x^2+38*x+1)) + O(x^100))

CROSSREFS

Cf. A000290, A005891, A129557, A254332.

Sequence in context: A209541 A279295 A053903 * A102807 A160131 A206691

Adjacent sequences:  A254330 A254331 A254332 * A254334 A254335 A254336

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Jan 28 2015

STATUS

approved

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Last modified July 29 13:28 EDT 2021. Contains 346346 sequences. (Running on oeis4.)